Chapter Comments

• This chapter has two main parts: the first on parametric curves and the second on polar curves. We have spent most of our time in calculus working with curves that are represented in Cartesian coordinates, usually as a function y=f(x) and occassionally an implicitly defined curve. But there are lots of curves that are not easily represented this way. This chapter offers two alternate ways of representing curves (and the corresponding methods for working with such representations). Ultimately, the hope is that you will be able to select and work with a representation that is convenient and appropriate for whatever curve you are faced with.

• For this chapter, in particular, we assume that you have some sort of graphing calculator or other graphing device (or computer software). You should practice graphing by hand AND with your calculator (each of those tools offers it own particular kind of insight); and you should think carefully about which tool is most appropriate for which situations.

Chapter Contents

• §11.1 Curves Defined by Parametric Equations

• §11.2 Tangents and Areas

• §11.3 Arc Length and Surface Area

• §11.4 Polar Coordinates

• §11.5 Areas and Lengths in Polar Coordinates

• §11.6, §11.7 Conic Sections and Conic Sections in Polar Coordinates

Chapter 11 Sample Test Items and Sample Solutions

This document is part of the Math 2433: Calculus and Analytic Geometry III course designed for the Independent Study Department in the College of Continuing Education at the University of Oklahoma, Norman.

Go to:

• Calculus III Syllabus

• Table of Contents for Chapter 12: Infinite Sequences and Series
• Table of Contents for Chapter 13: Vectors and the Geometry of Space
• Table of Contents for Chapter 14: Vector Functions